Optimal convergence rate for Maxwell–Landau–Lifschitz system

Abstract

Micromagnetic evolution is described by the Landau–Lifshitz equation. The equation is studied without the exchange field. We consider the case with quasi-static Maxwell's equations and a single Landau–Lifshitz equation as well. We use recently introduced numerical scheme conserving magnitude of the magnetization and prove better convergence rate to the solution. We illustrate the theoretical results on numerical examples.